📌 Today I Solved the N-Queens Problem Using Backtracking

Today, I dived into the N-Queens problem, a classic example of how backtracking can be used to solve constraint-based problems.

✅ What I Learned:

• The goal is to place N queens on an N x N chessboard so that no two queens threaten each other.

• I used backtracking to explore all possible placements, row by row, and only kept safe configurations.

• I learned how to represent each solution as a list where the index is the row and the value is the column (e.g., [1, 3, 0, 2]).

• I also wrote a helper function to visualize the chessboard, making it easier to understand and debug.

💡 Key Concepts Practiced:

• Recursive function design

• Backtracking logic

• Diagonal and vertical threat detection

• Clean board state management

• Visualization of board configurations

Below is the full working Python code I used:

def solve_n_queens(n):
    solutions = []
    board = []

    def is_safe(row, col):
        for r in range(row):
            c = board[r]
            if c == col or abs(c - col) == abs(r - row):
                return False
        return True

    def backtrack(row):
        if row == n:
            solutions.append(board[:])
            return
        for col in range(n):
            if is_safe(row, col):
                board.append(col)
                backtrack(row + 1)
                board.pop()

    backtrack(0)
    return solutions

# Example usage
n = 4
results = solve_n_queens(n)

def print_board(solution):
    for row in solution:
        line = ['.'] * n
        line[row] = 'Q'
        print(' '.join(line))
    print()

for sol in results:
    print_board(sol)